Question

Which of the following pairs has quantities of the same dimensions?
(a) Magnetic field B and magnetising field intensity H
(b) Magnetic field B and intensity of magnetisation I
(c) Magnetising field intensity H and intensity of magnetisation I
(d) Longitudinal strain and magnetic susceptibility

Answer 1

(c) Magnetising field intensity H and intensity of magnetisation I
(d) Longitudinal strain and magnetic susceptibility

Dimension of Magnetic field B is given by,
F=Bqv
$\Rightarrow$$B=\frac{F}{qv}$
$\Rightarrow$$\frac{\left[{\mathrm{MLT}}^{-2}\right]}{\left[\mathrm{AT}\right]\left[{\mathrm{LT}}^{-1}\right]}=\left[{\mathrm{MT}}^{-2}{\mathrm{A}}^{-1}\right]$
Dimension of magnetising field intensity H is given by,
H=$\left[\frac{Idl}{r^2}\right]$
$\Rightarrow$$\frac{\left[\mathrm{AL}\right]}{\left[{\mathrm{L}}^2\right]}=\left[{\mathrm{AL}}^{-1}\right]$
Dimension of intensity of magnetisation I is also $\left[{\mathrm{AL}}^{-1}\right]$ as both Magnetising field intensity H and intensity of magnetisation I are measured in Am^$-1$.
Hence, option (a) and option (b) is incorrect. Option (c) is correct.
As Longitudinal strain and magnetic susceptibility both are dimensionless quantity. Hence, option (d) is correct.